Dimensional
Analysis
Unit 1.3
Chapter 1 Section 2
What is dimensional analysis?
A
tool for converting from one unit to another

Equality = the quantity of two different units that
represent equal amounts
 Ex.

1 dollar = 4 quarters
Important equalities to remember:
1
kilo-____ = 1000 base units (base units = g, l, m)
 1 base unit = 1000 milli
 1 mL = 1 cm3
Rules for Dimensional Analysis
1.
2.
3.
4.
5.
Grams
ALL Numbers are written as fractions
Write everything WITH its unit (NO NAKED
numbers)
Arrange conversion factors so the
previous unit cancels (diagonal units)
Numbers on TOP are MULTIPLIED
Numbers on BOTTOM are DIVIDED
Liters
Conversion Factor
 To
convert from one unit to another you
need an equality
 When you write an equality as a fraction it
is called a conversion factor
Conversion Setup
Given # old units x new units
old units

Done properly the old units cancel out giving you the
amount in the new units
Practice Proper Setup
 What




are four equalities for time?
1 min = 60 seconds
1 hour = 60 min
I day = 24 hours
1 year = 12 months
Practice Proper Setup
 Convert
9 hours into minutes using
equalities

9hrs * 60min = 540 min *60 sec = 32,400sec
Dd
1 hrs
1 min
Practice
 If
John has 12 shillings, how many dollars is
that worth if 1 shilling equals 2 yen, 6 yen
equal 3 franks and 2 franks equal 4
dollars?

12 shillings * 2 yen = 24 yen * 3 franks =
1 shilling
6 yen
12 franks * 4 dollars = 24 dollars
2 franks
Practice
 If
you have 9 g of a substance that has a
density of 3g/mL, what is the volume of
the substance in milliliters?

9g * 1 mL = 3 mL
3g
Practice
A
corvette can travel 17.0 miles on one
gallon of gasoline. How many kilometers
per liter is this?

(1.61 km = 1 mile; 1 Liter = 0.264 gallon)

17 miles * 1.61 km = 27.37 km/gallon
1 gallon
1 miles